Existence of entire solutions to a fractional Liouville equation in Rn

Abstract

We study the existence of solutions to the problem D n 2u Qenu in Rn; V : Z Rn enu dx < l; where Q on 1! or Q on 1!. Extending the works of Wei-Ye and Hyder-Martinazzi to arbitrary odd dimension nb3 we show that to a certain extent the asymptotic behavior of u and the constant V can be prescribed simultaneously. Furthermore if Q n 1! then V can be chosen to be any positive number. This is in contrast to the case n 3, Q 2, where Jina "Maalaoui" Martinazzi "Xiong showed that necessarily V ajS3j, and to the case n 4, Q 6, where C-S. Lin showed that V ajS4j.